Ms. Quinn, the City Council speaker, quickly pivoted the conversation back to her plan to create more affordable housing.

Ms. Quinn, a Democrat, re-emerged this week as the putative front-runner in the race to be mayor, as Mr. Weiner’s standing in a poll tumbled after his acknowledgment that the sexually explicit online exchanges with women that prompted his resignation from Congress had continued through last summer.

Ms. Quinn now finds herself in an enviable, if precarious, position, with six weeks until the primary — an eternity in a topsy-turvy election season — and a roster of rivals eager to tear apart her record.

On Wednesday, a Republican candidate, John A. Catsimatidis, plans to begin running a television advertisement criticizing Ms. Quinn over a crime issue; she has already been the subject of a series of negative television advertisements financed by opponents of carriage horses in Central Park, and her Democratic opponents frequently criticize her support for rewriting term limits laws, which allowed Mayor Michael R. Bloomberg to seek a third term.

Ms. Quinn seemed in high spirits on Tuesday as she toured senior centers on the Upper East Side, joking with residents about bingo and punctuating autographs with a stock phrase, “Thanks for being a great New Yorker!” She shared stories of her grandmother, who lived in a Long Island senior center, saying her life was longer because of it.

“Every day she had a reason — when I was at school and my father was at work — to get up and get dressed,” she said. “It wasn’t just a meal. It was a second home, a community.”

Photo

City Council Speaker Christine C. Quinn at a news conference on Tuesday where she announced a plan to end co-pays for medications that treat chronic illnesses. She would not say whether she was worried that Anthony Weiner's declining popularity would help her opponents.Credit
Ángel Franco/The New York Times

At the Lenox Hill Neighborhood House, Abel Amar, 95, a former textile designer, asked Ms. Quinn if her fiery red hair was natural.

At the Carter Burden Luncheon Club and Senior Program, Linda Goldwater, a retired teacher, asked Ms. Quinn what she would give teachers in the next round of contract negotiations. “A fair deal,” Ms. Quinn said, sidestepping specifics.

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Ms. Quinn seemed eager to talk about anything other than Mr. Weiner and Mr. Spitzer, who have dominated national headlines in recent days. (Mr. Spitzer is running for city comptroller.)

Appearing on CNN on Tuesday morning, she said it would be “cheeky” to call for Mr. Weiner to drop out of the mayoral race. “Of course the scandal had an impact in voters’ minds,” she said. “You need a mayor who has a level of maturity and responsibility.”

Later, at a news conference announcing a plan to end co-pays for medications that treat chronic illnesses, Ms. Quinn would not say whether she was worried that Mr. Weiner’s declining popularity would help another Democratic opponent, Bill de Blasio, the public advocate.

“One thing you can bet your last dollar on,” she said, “is that polls are going to go up and down between now and Sept. 10.” She declined to say anything more.

But later, on MSNBC, Ms. Quinn took a shot at Mr. Spitzer, who resigned as governor over his patronizing of prostitutes but who suggested in a recent interview that Mr. Weiner’s behavior disqualified him from being mayor.

“I don’t think Eliot Spitzer is in a position to be pointing fingers at anybody,” she said.

A version of this article appears in print on July 31, 2013, on Page A18 of the New York edition with the headline: For Quinn, Topics
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